1. Field of the Invention
The present invention relates to computerized simulation of hydrocarbon reservoirs, and in particular to simulation of fluid flow in a complex heterogeneous subterranean reservoir where multiple interacting formation phenomena may be present, such as multimodal porosity or multi-scale fracture networks with spatially variable fluid transmissibilities.
2. Description of the Related Art
Many fluid-bearing subterranean reservoirs are naturally fractured. Interconnected fracture networks can have significant impact on the flow and transport phenomena within the porous medium. The use of dual porosity (DP) approach in reservoir simulation to represent fractured media has been in use in the petroleum industry since the mid-1970s. The basic concept of this approach can be schematically illustrated as in FIG. 1. FIG. 1 is a schematic diagram of such a dual porosity approach for fluid flow simulation in a naturally fractured reservoir which has vugs and fractures, as indicated at 10 and 12, respectively.
In this approach, the network of interconnected fractures was represented as grid cells 14 in the fracture continuum. The volume and inter-cell transmissibilities for the fracture cells are characterized to be representative of the fracture network. A collocated system of grid cells 14 known as a matrix 16 was used to represent the storage and transmissibilities of the intergranular pore space, also referred to as the matrix continuum. Since fracture transmissibilities are usually orders of magnitudes large than those of the matrix, early DP modeling considered the matrix grid cells as discontinuous and the cells were treated as sources or sinks to the fracture system. That is, for a DP model, a matrix cell had fluid exchanges with the collocated fracture cells, but the matrix inter-cell flow terms were considered to be small and negligible. To correctly describe the flow potentials between matrix and fracture, elaborate treatments of gravity, capillary, and viscous potentials usually had to be included in the matrix-fracture flow terms.
Later, as computer speed and memory increased, the dual permeability generalization was added where both the matrix system and the fracture system were considered to have through flow in addition to the local inter-porosity fluid exchanges. This class of model was referred to as dual-porosity dual-permeability (DPDP) model. However, there were sometimes extreme contrasts in porosity and permeability and rock-fluid properties such as different wettability, interfacial tension, relative permeabilities, capillary pressures, and fluid phase densities of the multiphase multicomponent fluid flow. Due to this, the dual-continuum model typically proved to be very challenging to solve numerically.
Further description of the DP and DPDP models can be found in articles which Applicant authored or co-authored in the literature: Larry S. K. Fung, “Numerical Simulation of Naturally Fractured Reservoirs” SPE (Society of Petroleum Engineers) paper 25616, April 1993; Larry S. K. Fung, “Simulation of Block-to-Block Processes in Naturally Fractured Reservoirs” SPE Reservoir Engineering, November, 1991, pp 477-484; and Larry S. K. Fung, David A. Collins, “An Evaluation of the Improved Dual Porosity Model for the Simulation of Gravity Effects in Naturally Fractured Reservoirs” Journal of Canadian Petroleum Technology, May-June 1991, Vol. 30, No. 3, pp 61-68.
In the mid-1990s, high performance computing using multi-processor parallel computers was increasingly applied to reservoir simulation. By the early 2000s, parallel dual-porosity dual-permeability reservoir simulation had emerged with methodologies primarily targeting structured grid, structured domain partitioning schemes, and structured solvers. The methods and algorithms in this simulator were described in: Tareq M. Al-Shaalan, Larry S. K. Fung, and Ali H. Dogru, “A Scalable Massively Parallel Dual-Porosity Dual Permeability Simulator for Fractured Reservoirs with Super-K Permeability” SPE Paper 84371, Oct 2003; and Larry S. K. Fung, Tareq M. Al-Shaalan, “Parallel Iterative Solver for the Dual Porosity Dual Permeability System in Fractured Reservoir Simulation, International Petroleum Technology Conference (IPTC) Paper 10343, November, 2005.
The DPDP simulator and associated solver method used in high performance computing of the types described above performed parallel simulation of fractured reservoir models which had millions of grid cells. However, so far as is known, the efforts were limited to structured grids and structured data partitions which were not optimal, particularly when a significant numbers of fracture cells were what are known as null cells. Null cells are finite volumes within the solution domain where the porosity and/or permeability are effectively zero.
Recent petrophysical analyses as well as core laboratory measurements have indicated that pore structures of many giant hydrocarbon-bearing carbonate reservoirs are complex and should be characterized as multi-modal. FIG. 2 illustrates the results of mercury injection capillary pressure (MICP) laboratory experiments on carbonate reservoir core samples. These data show pore structure which is characterized as multi-modal. More details can be found, for example, in: Ed Clerke et. al., “Application of Thomeer Hyperbolas to decode the pore systems, facies and reservoir properties of the Upper Jurassic Arab D Limestone, Ghawar field, Saudi Arabia: A Rosetta Stone Approach” GeoArabia, Vol. 13, No. 4, 2008, pp. 113-160.
The multi-modal pore system of these media indicates that lumping of all pore space within a grid cell into a homogeneous value of porosity and permeability is inadequate. At the same time, the fracture system can also be complex and multi-scale. For example, the fracture system can have several scales of fractures: micro, macro, and mega scale fracture sets.